Question
The greatest interger function is continuous on .
Answer :
Word Count : 123
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The statement is false. Let (f(x)=\lfloor x\rfloor) denote the greatest integer function. To examine continuity, consider any integer (n\in\mathbb{Z}). For (x\to n^{-}), we have (f(x)=n-1), so (\lim_{x\to n^{-}} f(x)=n-1). For (x\to n^{+}), we have (f(x)=n), so (\lim_{x\to n^{+}} f(x)=n).
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